Determining an encoding type of data

ABSTRACT

Implementations of the present disclosure provide for determining an encoding type of data. Implementations include receiving a data set from a computer-readable storage medium, decoding the data set using a first encoding type to provide a first plurality of numbers, generating a first distribution based on the first plurality of numbers, decoding the data set using a second encoding type to provide a second plurality of numbers, and generating a second distribution based on the second plurality of numbers. An actual encoding type of the data set is determined based on the first distribution, the second distribution and an expected distribution, and the data set is processed based on the actual encoding type.

BACKGROUND

In data processing, many computer languages require that arithmetic becarried out using standard formats and operations, such asfloating-point decimal. Interchange formats are provided for exchangingdata using a fixed length bit-string for a given interchange format.Encoding schemes are provided for the interchange formats, whichencoding schemes enable encoding of the sign, exponent, and significantas a compressed sequence.

SUMMARY

Implementations of present disclosure include methods of determining anencoding type of data. In some implementations, a method includesreceiving a data set from a computer-readable storage medium, decodingthe data set using a first encoding type to provide a first plurality ofnumbers, generating a first distribution based on the first plurality ofnumbers, decoding the data set using a second encoding type to provide asecond plurality of numbers, and generating a second distribution basedon the second plurality of numbers. An actual encoding type of the dataset is determined based on the first distribution, the seconddistribution and an expected distribution, and the data set is processedbased on the actual encoding type.

In some implementations, determining an actual encoding type includescomparing the first distribution to the expected distribution, comparingthe second distribution to the expected distribution, identifying atleast one of the first and second distributions as corresponding to theexpected distribution to provide an identified distribution, andselecting one of the first and second encoding types as the actualencoding type based on the identified distribution.

In some implementations, the method further includes determining a firsttest statistic based on the first distribution and the expecteddistribution, determining a second test statistic based on the seconddistribution and the expected distribution, and comparing each of thefirst test statistic and the second test statistic to a threshold,wherein selecting one of the first and second encoding types as theactual encoding type is based on a result of the comparing.

In some implementations, the first distribution corresponds to afrequency of values of a first digit of each number of the firstplurality of numbers, and the second distribution corresponds to afrequency of values of a second digit of each number of the secondplurality of numbers.

In some implementations, the method further includes determining thatboth the first distribution and the second distribution correspond tothe expected distribution, generating a third distribution based on thefirst plurality of numbers, generating a fourth distribution based onthe second plurality of numbers, and determining the actual encodingtype of the data set based on the third distribution, the fourthdistribution and a second expected distribution.

In some implementations, the actual encoding type includes one ofdensely packed decimal (DPD) encoding and binary encoding.

In some implementations, the expected distribution comprises a Benford'sdistribution.

The present disclosure also provides a computer-readable storage mediumcoupled to one or more processors and having instructions stored thereonwhich, when executed by the one or more processors, cause the one ormore processors to perform operations in accordance with implementationsof the methods provided herein.

The present disclosure further provides a system for implementing themethods provided herein. The system includes one or more processors, anda computer-readable storage medium coupled to the one or more processorshaving instructions stored thereon which, when executed by the one ormore processors, cause the one or more processors to perform operationsin accordance with implementations of the methods provided herein.

It is appreciated that methods in accordance with the present disclosurecan include any combination of the aspects and features describedherein. That is to say that methods in accordance with the presentdisclosure are not limited to the combinations of aspects and featuresspecifically described herein, but also include any combination of theaspects and features provided.

The details of one or more embodiments of the present disclosure are setforth in the accompanying drawings and the description below. Otherfeatures and advantages of the present disclosure will be apparent fromthe description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1A is a graph illustrating an exemplar first digit distribution.

FIG. 1B is a graph illustrating an exemplar second digit distribution.

FIG. 1C is a graph illustrating an exemplar third digit distribution.

FIG. 2A is a graph illustrating an exemplar first calculateddistribution in accordance with implementations of the presentdisclosure.

FIG. 2B is a graph illustrating an exemplar second calculateddistribution in accordance with implementations of the presentdisclosure.

FIG. 3A is a graph illustrating a comparison between the exemplardistribution of FIG. 1A and the exemplar distribution of FIG. 2A.

FIG. 3B is a graph illustrating a comparison between the exemplardistribution of FIG. 1A and the exemplar distribution of FIG. 2B.

FIG. 4 is a flowchart illustrating exemplar steps that can be executedto determine an encoding type in accordance with implementations of thepresent disclosure.

FIG. 5 is a flowchart illustrating exemplar steps that can be executedto compare calculated distributions to an expected distribution inaccordance with implementations of the present disclosure.

FIG. 6 is an exemplar environment for practical execution ofimplementations of the present disclosure.

FIG. 7 is a schematic illustration of exemplar computer systems that canbe used to execute implementations of the present disclosure.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

In computer processing, floating-point refers to a system of numericalrepresentation, in which a string of digits represents a rationalnumber. A numerical representation specifies a way of electronicallystoring a number that may be encoded as a string of digits. The term“floating-point” indicates that a radix point (e.g., a decimal point, ora binary point) can “float,” or can be placed anywhere relative to thedigits of the number. The position of the radix point is indicatedseparately in the internal representation. Logically, a floating-pointnumber includes a signed digit string of a given length in a given base,and a signed integer exponent, also referred to as the characteristic orscale, which modifies the magnitude of the number. An advantage offloating-point representation, over other representations (e.g.,fixed-point, and integer) is that it can support a much wider range ofvalues. Although the floating-point representation needs slightly morestorage to encode the position of the radix point, floating-pointrepresentations achieve a greater value range.

Over the last few decades, several standards have defined floating-pointrepresentations used in computer processing. One traditional standardprovides a plurality of binary formats and for representingfloating-point numbers. More recently, such standards have been expandedto further include a plurality of decimal formats for representingfloating-point numbers. These standards can implement exchange encodingsincluding a binary encoding and a decimal encoding (e.g., densely packeddecimal (DPD) encoding). The implementation of different formats (e.g.,binary and decimal formats) and encodings (e.g., binary and decimalencodings) presents various issues when processing data from disparatesystems. For example, it may not be immediately clear whether aparticular floating-point data set has been encoded using binaryencoding or decimal encoding.

The present disclosure enables a data set to be analyzed to distinguishbetween binary and decimal encodings based on statistical distributions.In a specific implementation, the present disclosure enables a data setof decimal floating-point numbers to be analyzed to distinguish betweenbinary and DPD encodings. To achieve this, it is initially determinedthat the data set is representative of decimal floating-point data ofknown length. That is to say, that the number of data values, or numberin the data set is known. Such data sets are presented for execution ofa particular procedure. Based on the context of the procedure, it can bedetermined that the data set includes decimal floating-point data, asopposed to text data, integer data, and/or special format data (e.g., aword processing document, or a presentation document), for example.Although the data set includes decimal floating-point data of knowlength, the particular encoding type that was used to encode the dataset remains uncertain.

To determine which encoding was used to encode a particular data set,implementations of the present disclosure compare observed, orcalculated distributions to a theoretical, or expected distribution.Although the present disclosure is provided in the context of theexpected distribution being the Benford's distribution, it isappreciated that principles of the present disclosure can be implementedusing other distributions, and is not limited to the Benford'sdistribution.

The Benford's distribution is based on Benford's law, which providesthat the leading digit of the numbers in a list of numbers isdistributed in a specific, non-uniform way. More specifically, the firstdigit of a multi-digit number has a value of “1” almost one third of thetime, and larger values occur as the first digit with decreasingfrequency. FIG. 1A illustrates an exemplar distribution (Benford'sdistribution) for the first digit of a multi-digit number. As seen inFIG. 1A, “1” is the first digit approximately 30% of the time, and “9”is the first digit less than 5% of the time. This distribution of firstdigits arises logically whenever a set of values is distributedlogarithmically. More specifically, Benford's law provides that theleading digit d (dε{1, . . . , b−1}) in base b (b≧2) occurs with thefollowing probability (P):

$\begin{matrix}{{P(d)} = {{{\log_{b}\left( {d + 1} \right)} - {\log_{b}(d)}} = {\log_{b}\left( {1 + \frac{1}{d}} \right)}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

This quantity is exactly the space between d and d+1 in a logarithmicscale. In base 10, the leading, or first digits have the exemplarBenford's distribution of FIG. 1A.

Benford's law can be extended to digits beyond the first digit. Morespecifically, the probability of encountering a number starting with thestring of digits “n” is provided by:

$\begin{matrix}{{{\log_{10}\left( {n + 1} \right)} - {\log_{10}(n)}} = {{\log_{10}\left( {1 + \frac{1}{n}} \right)}.}} & {{Equation}\mspace{14mu} 2}\end{matrix}$This equation is provided using base 10 (i.e., b=10). The above equationcan be used to determine the probability that a particular value occursat a particular position within a number. For example, the probabilitythat a “2” is encountered as the second digit is provided as:

$\begin{matrix}{{{\log_{10}\left( {1 + \frac{1}{12}} \right)} + {\log_{10}\left( {1 + \frac{1}{22}} \right)} + \ldots + {\log_{10}\left( {1 + \frac{1}{92}} \right)}} \approx {0.109.}} & {{Equation}\mspace{14mu} 3}\end{matrix}$FIGS. 1B and 1C illustrate exemplar distributions (Benford'sdistributions) for the second and thirds digit of a multi-digit number,respectively. As evidenced in FIG. 1C, the distribution of the n^(th)digit, as n increases, approaches a uniform distribution ofapproximately 10% for each of the ten possible digits.

As discussed above, implementations of the present disclosure compareobserved, or calculated distributions to a theoretical, or expecteddistribution to determine the encoding type of a particular data set.Initially, a first encoding type, either decimal encoding (e.g., DPD),or binary encoding (e.g.,), is assumed. The data set is decoded usingthe presumed first encoding type, and a list of floating-point numbersis provided from the data set. A first calculated distribution iscalculated based on a common digit (e.g., the first digit) of each ofthe numbers of the data set. In the case of decimal encoding, thedistribution can be provided as “distribution_DEC.” and the distributioncan be provided as “distribution_BIN,” for binary encoding. FIG. 2Aillustrates an exemplar first calculated distribution based on the firstdigits of a list of numbers generated using the first encoding type.

Subsequently, a second encoding type (the other of either decimalencoding, or binary encoding) is assumed. The data set is decoded usingthe presumed second encoding type, and a list of floating-point numbersis provided from the data set. A second calculated distribution iscalculated based on a digit having a particular position within each ofthe numbers of the data set (e.g., the first digit). FIG. 2B illustratesan exemplar second calculated distribution based on the first digit ofeach of the numbers in the list of numbers generated using the secondencoding type.

Each of the first and second calculated, or observed distributions iscompared to the expected first digit distribution, the first digitBenford's distribution in the present example. FIGS. 3A and 3Billustrates comparisons of the Benford's distribution of FIG. 1A to eachof the first and second calculated distributions, respectively. Theencoding type corresponding to the calculated distribution that isdeemed to correspond to, or otherwise be a good fit to the Benford'sdistribution can be identified as the proper encoding type of the dataset. In the exemplar, comparisons of FIGS. 3A and 3B, the firstcalculated distribution has a better fit to the Benford's distribution.Consequently, the first encoding type is identified as the encoding typeof the subject data set.

If the list of numbers of the data set is of sufficient length, thedistributions of the second and third digits can be evaluated in view ofthe corresponding Benford's distributions (e.g., Benford's distributionsof FIGS. 1B and 1C, respectively). However, as the list becomes longer,and more digits besides the first digit are taken into account, thecomputational effort correspondingly increases. Consequently, anappropriate balance between accuracy of the result and the calculationeffort should be considered.

Generally, the list of numbers should be greater than a threshold (e.g.,at least 109 numbers long). More specifically, a common criterion forthe minimum amount of data in each class is that there should be atleast 5 values. For the Benford's distribution, in particular example, ashare of 0.046 of all first digits to have the value 9 can be expected,which is the lowest probability of all of the other digits (i.e., 1-8).To ensure at least 5 values to be in the digit class ‘9’, one needs atleast 5/0.046=1.09 numbers in the list of numbers. For the distributionof the second and third digit, a slightly smaller minimum length of thenumber list is provided, because the distribution of these digitsapproaches a uniform distribution (e.g., 0.10 (or 10%) for each digitbetween 0 and 9). Consequently, a practical implementation of thepresent disclosure could only consider the first and/or the seconddigits.

In other implementations, a sequence of digits could be analyzed, forexample, the first two digits, or the first three digits. Such ananalysis can be achieved implementing Equation 3, for example. By way ofnon-limiting example, the digit sequence ‘999’ has a probability of4.3×10⁻⁴, whereas the digit sequence ‘100’ has a probability of4.3×10⁻². Accordingly, the digit sequence ‘100’ is 100 times more likelyto occur in a given list of numbers than the digit sequence ‘999’. Ifconsidering a digit sequence including only the first two digits,approximately 1,000 numbers should be included in the number list toprovide a sufficiently accurate distribution. If considering a sequenceof digits including the first three digits, approximately 10,000 numbersshould be included in the number list to provide a sufficiently accuratedistribution. These thresholds (i.e., 1,000 and 10,000) are merelyexemplar in nature, and implementations of the present disclosure arenot limited to these values.

In one exemplar, practical implementation of digit sequences, it may bepossible to compute values of an expected distribution for numbers of acertain data type (e.g., that may not comply with the Benford'sdistribution). By way of one non-limiting example, it may be known thatnumbers representing a product may have three non-zero digits at thebeginning, two to six zero digits, and two to six non-zero digits at theend. It may be possible to either enter such expected distributionsmanually, or to analyze one or more digit sequences (e.g., the firstthree digits, the middle two to six digits, and/or the last two to sixdigits) to obtain such expected distributions.

By way of non-limiting example, the chi-square distribution can beimplemented to compare the calculated distributions to the Benford'sdistribution. More specifically, the chi-square distribution can beimplemented in the framework of a chi-square test for goodness of fit ofan observed distribution to a theoretical, or expected distribution. Inthe present disclosure, the chi-square distribution can be implementedto provide a chi-square test for goodness of fit of each of thecalculated distributions (i.e., the observed distribution) to theBenford's distribution (i.e., the theoretical distribution). Morespecifically, the chi-square test for goodness of fit can be implementedto test association of variables in two-way tables where thetheoretical, or expected distribution is evaluated against the observeddistribution. The chi-square test statistic is provided as:

$\begin{matrix}{X^{2} = {\sum\limits_{\;}^{\;}\frac{\left( {{observed} - {expected}} \right)^{2}}{expected}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

If the chi-square test statistic is large, the observed and expectedvalues are not close and the model is a poor fit to the data. If thechi-square test statistic is small, the observed and expected values areclose and the model is a good fit to the data. In the presentdisclosure, a chi-square test statistic is determined for each of thecalculated distributions with respect to the Benford's distribution.Consequently, a first chi-square test statistic, statistic_DEC (X_(DEC)²), and a second chi-square test statistic, statistic_BIN (X_(BIN) ²),are calculated for the given data set. Each of the statistic_DEC andstatistic_BIN can initially be compared to a so-called cut-off, orthreshold value. The threshold value can be determined in a known mannerbased on a so-called significance value (α), and the degrees of freedomof the calculated distribution. Exemplar significance values caninclude, but are not limited to, 0.10, 0.05, and 0.01. The significancevalue provides a confidence level, and indicates how many analyses outof a given number of different analyses will yield an incorrect result.For example, if α is equal to 0.05, one analysis out of twenty analyseswill be incorrect (e.g., a 5% error rate). As another example, if α isequal to 0.10, one analysis out of ten analyses will be incorrect (e.g.,a 10% error rate). Generally, the threshold value can be determined fromstandard tables based on a given probability P, which can be determinedas P=1−α, and further based on a given degree of freedom of the chisquare distribution. An exemplar threshold would be 15.51 for 8 degreesof freedom and α=0.05. An exemplar table can be found in the “Handbookof Mathematics,” by I. N. Bronshtein and K. A. Semendyayev, Springer,3rd edition (May 16, 1997), for example.

If both the statistic_DEC, or the statistic_BIN is greater than thethreshold value (e.g., 1.5.51), neither of the calculated distributionsis deemed to be a good fit, or otherwise correspond to the Benford'sdistribution. Consequently, an alternative method could be pursued todetermine the encoding type of the data set. If the statistic_DEC isless than the threshold, and the statistic_BIN is greater than thethreshold, the distribution_DEC is deemed to be a good fit, or otherwisecorrespond to the Benford's distribution. In such a case, the decimalencoding is selected as the encoding type of the data set. If thestatistic_BIN is less than the threshold, and the statistic_DEC isgreater than the threshold, the distribution_BIN is deemed to be a goodfit, or otherwise correspond to the Benford's distribution. In such acase, the binary encoding is selected as the encoding type of the dataset.

In some cases, both the statistic_DEC and the statistic_BIN are lessthan the threshold. Consequently, both the distribution_DEC and thedistribution_BIN is deemed to be a good fit to the Benford'sdistribution. In one implementation, because both of the calculateddistributions are deemed to be a good fit, neither encoding can bedetermined to be the encoding type of the data set. In otherimplementations, the statistic_DEC and the statistic_BIN can be furtheranalyzed to determine which encoding is the appropriate encoding. By wayof one non-limiting example, the test statistic having the lowest valuecould be deemed to be a better fit, and the corresponding encoding canbe determined to be the encoding type of the data set. In otherimplementation, further analysis could be implemented using otherstatistical methods such as the Kolmogorow-Smimow test.

If neither encoding can be deemed to be the encoding type of the dataset based on the test statistics calculated for the first digitdistribution, the second, third and/or other subsequent digits, or asequence of digits can be processed in accordance with the abovemethodology. More specifically, calculated distributions for the seconddigit can be calculated and compared to the expected distribution forsecond digits (e.g., the second digit Benford's distribution of FIG.1B). Chi-square test statistics can be calculated based on thecalculated distributions for the second digit, and the encoding typecould be determined based thereon. Calculated distributions forsubsequent digits (e.g., the third digit), or sequence of digits couldalso be calculated and compared to the expected distribution for thecorresponding subsequent digit (e.g., the third digit Benford'sdistribution of FIG. 1C), or sequence of digits. Chi-square teststatistics can be calculated based on the calculated distributions forthe subsequent digit(s), and the encoding type could be determined basedthereon.

Referring now to FIG. 4, a flowchart illustrates exemplar steps that canbe executed in accordance with implementations of the presentdisclosure. In step 400, a data set is retrieved. In step 402, it isdetermined whether the data contained in the data set includesfloating-point decimal data. If the data does not include floating-pointdecimal data, the flowchart continues in step 404. If the data doesinclude floating-point decimal data, the flowchart continues in step406. In step 404, an alternative method to determine the encoding typeof the data set can be implemented, and the flowchart ends.

An exemplar alternative method can determining the number of bitcombinations provided in the data set. For example, DPD encoding usesonly 1000 out of 1024 bit combinations for each group of three digits.If one or more bit combinations in the data set is undefined in DPDencoding, the actual encoding type must be binary. Still anotherexemplar alternative method can include analyzing range of numbers ofthe data set. More specifically, the range of numbers that can berepresented by decimal floating-point numbers is significantly largerthan that expected in real data sets. For example, for 64-bit decimalfloating-point, the range of numbers is approximately 10⁻³⁸³ to 10³⁸⁴.Depending on the application, a criterion can be defined. An exemplarcriterion can include: If a number that is larger than 10²⁰, or smallerthan 10⁻²⁰ is present in the data set, it can be assumed that the wrongencoding type was used to decode the data set. The appropriate upper andlower threshold values will depend on the application.

In step 406, it is determined whether the data set includes sufficientdata points. In other words, it is determined whether the list ofnumbers provided in the data set is of sufficient length to determineaccurate distributions. If the data set does not include a sufficientnumber of data points, the flowchart continues in step 404, as discussedabove. If the data points do include a sufficient number of data points,the data is decoded presuming a first encoding type in step 408. In step410, a first distribution (e.g., the exemplar first calculateddistribution of FIG. 2A) is determined based on the decoded data. Instep 412, the data is decoded presuming a second encoding type. In step414, a second distribution (e.g., the exemplar second calculateddistribution of FIG. 2B) is determined based on the decoded data.

In step 416, the first and second calculated distributions are eachcompared to an expected distribution (e.g., the Benford's distribution).In step 418, it is determined whether both calculated distributions areconsistent with, or are otherwise good fits with the expecteddistribution. If both calculated distributions are a good fit with theexpected distribution, the flowchart continues in step 404, as discussedabove. In other implementations, however, further processing of thecalculated distributions could be implemented to determine the encodingtype, if both calculated distributions are a good fit. In otherimplementations, other calculated distributions (e.g., for the secondand/or third) can be calculated and processed to determine the encodingtype, if both of the already determined calculated distributions are agood fit.

In step 420, it is determined whether the first distribution isconsistent with, or is otherwise a good fit to the expecteddistribution. If the first distribution is consistent with the expecteddistribution, the flowchart continues in step 422. If the firstdistribution is not consistent with the expected distribution, theflowchart continues in step 424. In step 422, the first encoding type isselected as the encoding type, and the flowchart ends. In step 424, itis determined whether the second distribution is consistent with, or isotherwise a good fit to the expected distribution. If the seconddistribution is consistent with the expected distribution, the flowchartcontinues in step 426. If the second distribution is not consistent withthe expected distribution, the flowchart continues in step 404, asdiscussed above. In step 426, the second encoding type is selected asthe encoding type, and the flowchart ends.

Referring now to FIG. 5, a flowchart illustrates exemplar steps that canbe executed to achieve the distribution comparisons in accordance withimplementations of the present disclosure. In step 500, a first teststatistic is calculated based on the first calculated distribution andthe expected distribution. In step 502, a second test statistic iscalculated based on the second calculated distribution and the expecteddistribution. In step 504, it is determined whether both the first andsecond test statistics is greater than the threshold, or cut-off. Ifboth the first and second test statistics are greater than thethreshold, neither the first calculated distribution nor the secondcalculated distribution is deemed to be a good fit to the expecteddistribution, and the flowchart continues in step 506. If at least oneof the first and second test statistics is greater than the threshold,at either the first calculated distribution or the second calculateddistribution is deemed to be a good fit to the expected distribution,and the flowchart continues in step 508. In step 506, an alternativemethod can be implemented to determine the encoding type, and theflowchart ends.

In step 508, it is determined whether both the first and second teststatistics is less than the threshold. If both the first and second teststatistics are less than the threshold, both the first and secondcalculated distributions are deemed to be a good fit to the expecteddistribution, and the flowchart continues in step 506, discussed above.In other implementations, however, further processing of the calculateddistributions could be implemented to determine the encoding type, ifboth calculated distributions are a good fit. In other implementations,other calculated distributions and corresponding test statistics (e.g.,for the second and/or third) can be calculated and processed todetermine the encoding type, if both of the already determinedcalculated distributions are a good fit.

If both the first and second test statistics are not less than thethreshold, only one test statistic is less than the threshold, and theflowchart continues in step 510. In step 510, it is determined whetherthe first test statistic is greater than the threshold. If the firsttest statistic is not greater than the threshold, the flowchartcontinues in step 512. If the first test statistic is greater than thethreshold, the flowchart continues in step 514. In step 512, the firstencoding type is selected as the encoding type, and the flowchart ends.In step 514, the second encoding type is selected as the encoding type,and the flowchart ends.

Referring now to FIG. 6, an exemplar environment 600 is illustrated, inwhich encoding type determination in accordance with the presentdisclosure can be implemented. The exemplar environment 600 can beimplemented to migrate stored data, for example, and includes a sourcedatabase 602, a target database 604, an administrator computer 606, anda network. Each of the source database 602, the target database 604 andthe administrator computer 606 can communicate with one another throughthe network 608. The network 608 can include, but is not limited to, alocal area network (LAN), a wide area network (WAN), a wireless LAN(WLAN), a metropolitan area network (MAN), a personal area network(PAN), the Internet, and/or combinations thereof.

In an exemplar implementation, an administrator using the administratorcomputer 606 seeks to transfer one or more data sets from the sourcedatabase 602 to the target database 604. The administrator, however, maybe unaware of the particular coding type that was used to encode thedata sets at the source database 602. For example, the data stored inthe target database may be required to be encoded using a particularformat. Consequently, the administrator should initially determine whatencoding was used to encode the data sets stored in the source database602. If that encoding type conforms to the encoding type used for thetarget database 604, to which the data set is to be transferred, thetransfer can occur without further manipulation of the data set. If,however, the encoding type used for the source database 602 does notconform to that of the target database 604, the administrator shouldconvert the encoding format before during transfer of the data set tothe target database 604.

Implementations of the present disclosure can be employed to determinethe encoding type of the data sets stored in the source database. Morespecifically, and by way of non-limiting example, the administrator canuse the administrator computer 606 to process one or more data sets inaccordance with the present disclosure. In short, the administratorcomputer can be used to process the data set(s), to calculate thecalculated distributions, and to compare the calculated distributions tothe expected distribution. Upon determining the encoding type of thedata set(s), the administrator computer can further be implemented toautomatically convert the encoding prior to transferring the data set(s)to the target database, such as in the case where the encoding type ofthe source database 602 is different to that of the target database 604.

Practical execution of implementations of the present disclosure are notlimited to the database migration scenario discussed above withreference to FIG. 6. Other scenarios can include, but are not limitedto, a web-based application executed using a client that implements afirst encoding type receiving data from a data source (e.g., anapplication server) that implements a second encoding type, and/orreading data using a processor that implements a first encoding typefrom an archive that stores the data using a second encoding type.

Referring now to FIG. 7, a schematic diagram of an exemplar computersystem 700 is provided. The system 700 can be used for the operationsdescribed in association with the methods described with reference toFIGS. 1A-6 according to one implementation. The system 700 includes aprocessor 710, a memory 720, a storage device 730, and an input/outputdevice 740. Each of the components 710, 720, 730, and 740 areinterconnected using a system bus 750. The processor 710 is operable toprocess instructions for execution within the system 700. In oneimplementation, the processor 710 is a single-threaded processor. Inanother implementation, the processor 710 is a multi-threaded processor.The processor 710 is capable of processing instructions stored in thememory 720 or on the storage device 730 to display graphical informationfor a user interface on the input/output device 740.

The memory 720 stores information within the system 700. In oneimplementation, the memory 720 is a computer-readable medium. In oneimplementation, the memory 720 is a volatile memory unit. In anotherimplementation, the memory 720 is a non-volatile memory unit. Thestorage device 730 is operable to provide mass storage for the system700. In one implementation, the storage device 730 is acomputer-readable medium. In various different implementations, thestorage device 730 may be a floppy disk device, a hard disk device, anoptical disk device, or a tape device. The input/output device 740provides input/output operations for the system 700. In oneimplementation, the input/output device 740 includes a keyboard and/orpointing device. In another implementation, the input/output device 740includes a display unit for displaying graphical user interfaces.

The features described can be implemented in digital electroniccircuitry, or in computer hardware, firmware, software, or incombinations of them. The apparatus can be implemented in a computerprogram product tangibly embodied in an information carrier, e.g., in amachine-readable storage device, for execution by a programmableprocessor; and method steps can be performed by a programmable processorexecuting a program of instructions to perform functions of thedescribed implementations by operating on input data and generatingoutput. The described features can be implemented advantageously in oneor more computer programs that are executable on a programmable systemincluding at least one programmable processor coupled to receive dataand instructions from, and to transmit data and instructions to, a datastorage system, at least one input device, and at least one outputdevice. A computer program is a set of instructions that can be used,directly or indirectly, in a computer to perform a certain activity orbring about a certain result. A computer program can be written in anyform of programming language, including compiled or interpretedlanguages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment.

Suitable processors for the execution of a program of instructionsinclude, by way of example, both general and special purposemicroprocessors, and the sole processor or one of multiple processors ofany kind of computer. Generally, a processor will receive instructionsand data from a read-only memory or a random access memory or both. Theessential elements of a computer are a processor for executinginstructions and one or more memories for storing instructions and data.Generally, a computer will also include, or be operatively coupled tocommunicate with, one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as EPROM, EEPROM, and flashmemory devices; magnetic disks such as internal hard disks and removabledisks; magneto-optical disks; and CD-ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,ASICs (application-specific integrated circuits).

To provide for interaction with a user, the features can be implementedon a computer having a display device such as a CRT (cathode ray tube)or LCD (liquid crystal display) monitor for displaying information tothe user and a keyboard and a pointing device such as a mouse or atrackball by which the user can provide input to the computer.

The features can be implemented in a computer system that includes aback-end component, such as a data server, or that includes a middlewarecomponent, such as an application server or an Internet server, or thatincludes a front-end component, such as a client computer having agraphical user interface or an Internet browser, or any combination ofthem. The components of the system can be connected by any form ormedium of digital data communication such as a communication network.Examples of communication networks include, e.g., a LAN, a WAN, and thecomputers and networks forming the Internet.

The computer system can include clients and servers. A client and serverare generally remote from each other and typically interact through anetwork, such as the described one. The relationship of client andserver arises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

In addition, the logic flows depicted in the figures do not require theparticular order shown, or sequential order, to achieve desirableresults. In addition, other steps may be provided, or steps may beeliminated, from the described flows, and other components may be addedto, or removed from, the described systems. Accordingly, otherimplementations are within the scope of the following claims.

A number of implementations of the present disclosure have beendescribed. Nevertheless, it will be understood that variousmodifications may be made without departing from the spirit and scope ofthe present disclosure. Accordingly, other implementations are withinthe scope of the following claims.

1. A computer-implemented method of determining an encoding type ofdata, the computer-implemented method being executed using one or moreprocessors and comprising: receiving a data set from a computer-readablestorage medium; decoding, using the one or more processors, the data setusing a first encoding type to provide a first plurality of numbers;generating, using the one or more processors, a first distribution basedon the first plurality of numbers; decoding, using the one or moreprocessors, the data set using a second encoding type to provide asecond plurality of numbers; generating, using the one or moreprocessors, a second distribution based on the second plurality ofnumbers; determining, using the one or more processors, an actualencoding type of the data set based on the first distribution, thesecond distribution and an expected distribution; and processing, usingthe one or more processors, the data set based on the actual encodingtype.
 2. The computer-implemented method of claim 1, wherein determiningan actual encoding type comprises: comparing the first distribution tothe expected distribution; comparing the second distribution to theexpected distribution; identifying at least one of the first and seconddistributions as corresponding to the expected distribution to providean identified distribution; and selecting one of the first encoding typeand the second encoding type as the actual encoding type based on theidentified distribution.
 3. The computer-implemented method of claim 1,further comprising: determining a first test statistic based on thefirst distribution and the expected distribution; determining a secondtest statistic based on the second distribution and the expecteddistribution; and comparing each of the first test statistic and thesecond test statistic to a threshold, wherein selecting one of the firstencoding type and the second encoding type as the actual encoding typeis based on a result of the comparing.
 4. The computer-implementedmethod of claim 1, wherein the first distribution corresponds to afrequency of values of a first digit of each number of the firstplurality of numbers, and the second distribution corresponds to afrequency of values of a second digit of each number of the secondplurality of numbers.
 5. The computer-implemented method of claim 1,further comprising: determining that both the first distribution and thesecond distribution correspond to the expected distribution; generatinga third distribution based on the first plurality of numbers; generatinga fourth distribution based on the second plurality of numbers; anddetermining the actual encoding type of the data set based on the thirddistribution, the fourth distribution and a second expecteddistribution.
 6. The computer-implemented method of claim 1, wherein theactual encoding type includes one of a decimal encoding and a binaryencoding.
 7. The computer-implemented method of claim 1, wherein theexpected distribution comprises a Benford's distribution.
 8. Anon-transitory computer-readable storage medium coupled to one or moreprocessors and having instructions stored thereon which, when executedby the one or more processors, cause the one or more processors toperform operations for determining an encoding type of data, theoperations comprising: receiving a data set from a remotecomputer-readable storage medium; decoding the data set using a firstencoding type to provide a first plurality of numbers; generating afirst distribution based on the first plurality of numbers; decoding thedata set using a second encoding type to provide a second plurality ofnumbers; generating a second distribution based on the second pluralityof numbers; determining an actual encoding type of the data set based onthe first distribution, the second distribution and an expecteddistribution; and processing the data set based on the actual encodingtype.
 9. The non-transitory computer-readable storage medium of claim 8,wherein determining an actual encoding type comprises: comparing thefirst distribution to the expected distribution; comparing the seconddistribution to the expected distribution; identifying at least one ofthe first and second distributions as corresponding to the expecteddistribution to provide an identified distribution; and selecting one ofthe first encoding type and the second encoding type as the actualencoding type based on the identified distribution.
 10. Thenon-transitory computer-readable storage medium of claim 8, wherein theoperations further comprise: determining a first test statistic based onthe first distribution and the expected distribution; determining asecond test statistic based on the second distribution and the expecteddistribution; and comparing each of the first test statistic and thesecond test statistic to a threshold, wherein selecting one of the firstencoding type and the second encoding type as the actual encoding typeis based on a result of the comparing.
 11. The non-transitorycomputer-readable storage medium of claim 8, wherein the firstdistribution corresponds to a frequency of values of a first digit ofeach number of the first plurality of numbers, and the seconddistribution corresponds to a frequency of values of a second digit ofeach number of the second plurality of numbers.
 12. The non-transitorycomputer-readable storage medium of claim 8, wherein the operationsfurther comprise: determining that both the first distribution and thesecond distribution correspond to the expected distribution; generatinga third distribution based on the first plurality of numbers; generatinga fourth distribution based on the second plurality of numbers; anddetermining the actual encoding type of the data set based on the thirddistribution, the fourth distribution and a second expecteddistribution.
 13. The non-transitory computer-readable storage medium ofclaim 8, wherein the actual encoding type includes one of a decimalencoding and a binary encoding.
 14. The non-transitory computer-readablestorage medium of claim 8, wherein the expected distribution comprises aBenford's distribution.
 15. A system for determining an encoding type ofdata, comprising: one or more processors; and a computer-readablestorage device coupled to the one or more processors, and havinginstructions stored thereon which, when executed by the one or moreprocessors, cause the one or more processors to perform operations fordetermining an encoding type of data, the operations comprising:receiving a data set from a remote computer-readable storage medium;decoding the data set using a first encoding type to provide a firstplurality of numbers; generating a first distribution based on the firstplurality of numbers; decoding the data set using a second encoding typeto provide a second plurality of numbers; generating a seconddistribution based on the second plurality of numbers; determining anactual encoding type of the data set based on the first distribution,the second distribution and an expected distribution; and processing thedata set based on the actual encoding type.
 16. The system of claim 15,wherein determining an actual encoding type comprises: comparing thefirst distribution to the expected distribution; comparing the seconddistribution to the expected distribution; identifying at least one ofthe first and second distributions as corresponding to the expecteddistribution to provide an identified distribution; and selecting one ofthe first encoding type and the second encoding type as the actualencoding type based on the identified distribution.
 17. The system ofclaim 15, wherein the operations further comprise: determining a firsttest statistic based on the first distribution and the expecteddistribution; determining a second test statistic based on the seconddistribution and the expected distribution; and comparing each of thefirst test statistic and the second test statistic to a threshold,wherein selecting one of the first encoding type and the second encodingtype as the actual encoding type is based on a result of the comparing.18. The system of claim 15, wherein the first distribution correspondsto a frequency of values of a first digit of each number of the firstplurality of numbers, and the second distribution corresponds to afrequency of values of a second digit of each number of the secondplurality of numbers.
 19. The system of claim 15, wherein the operationsfurther comprise: determining that both the first distribution and thesecond distribution correspond to the expected distribution; generatinga third distribution based on the first plurality of numbers; generatinga fourth distribution based on the second plurality of numbers; anddetermining the actual encoding type of the data set based on the thirddistribution, the fourth distribution and a second expecteddistribution.
 20. The system of claim 15, wherein the actual encodingtype includes one of a decimal encoding and a binary encoding.
 21. Thesystem of claim 15, wherein the expected distribution comprises aBenford's distribution.